Now it happends, the Server \\Server_1 is down and the share offline is not accessible anymore

You will notice that all the mapped drives O;N;S are offline and not accessible anymore even though the other Servers are reachable via Ping

Here is the Reason:

The Offline Files feature does not distinguish DFS paths from UNC paths. This can cause the Vista / Windows 7 client to interpret the entire namespace as unavailable if a target is down when a Vista / Windows 7 client attempts to access it. For example, if \\Contoso.com\Public is a domain-based root with several root targets and numerous links, the Offline Files feature interprets this namespace as a single server named \\Contoso.com. If a client is accessing or attempts to access the target Offline in the \\Contoso.com\Public namespace, and the target is unavailable, the Vista / Windows 7 client interprets the entire namespace as unavailable and will attempt to open a user’s locally cached files (if they exist). The Vista / Windows 7 client cannot access any target (in our example: Nosync & Sales & Offline) in the namespace until the target comes back online. The Vista / Windows 7 client will check every 2 minutes to detect whether the target has come back online.

What to do to avoid this:

- Use the NetBIOS Name or FQDN of the Target Server for mapping the Offline Files Share

you might best configure the Offline Files thresholds in group policy. There you can adjust when the PC will go offline based on throughput and latency on shares, DFS paths, all the way down to subfolders, etc.